5 - Contour lines of the Gaussian distribution PDF

5 - Contour lines of the Gaussian distribution PDF

Assignment objective

• Generate a plot of contour lines of the normal distribution's probability density function and state corresponding density values.
• Consider all edge cases.

Assignment implementation

Gaussian distribution

Normal distribution is a type of continuous probability distribution for multivariate random variables. It has two parameters: mean and variance.

Let's recall what is probability density function. Essentially, it's a function which at any given point returns relative likelihood that the value of the random variable would equal that point. Usually PDF is used to specify a probability of a random variable falling within a particular range. Integral over entire space is equal to 1.

Now the probability density function of the Gaussian distribution has the following form:

Contour lines

What are contour lines of a function? Well, the function value at each point of a contour line is the same. Our task is to plot contour lines of the probability density function defined above.

Below are 3D plots of PDF for different parameters alongside with contour lines.

And here heatmaps go:

Shiny

The 3D plots are available at Shiny. Don't miss a chance to fiddle about with covariance matrices by yourself!